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Simplifying (3 + 6i)(3 + 6i) = 0 Multiply (3 + 6i) * (3 + 6i) (3(3 + 6i) + 6i * (3 + 6i)) = 0 ((3 * 3 + 6i * 3) + 6i * (3 + 6i)) = 0 ((9 + 18i) + 6i * (3 + 6i)) = 0 (9 + 18i + (3 * 6i + 6i * 6i)) = 0 (9 + 18i + (18i + 36i2)) = 0 Combine like terms: 18i + 18i = 36i (9 + 36i + 36i2) = 0 Solving 9 + 36i + 36i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + 4i + 4i2) = 0 Factor a trinomial. 9((1 + 2i)(1 + 2i)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {-0.5, -0.5}
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